Ukr. Mat. Zh. - 2004. - 56, № 6. - pp. 737–744
We prove a general theorem on gluing of quasisymmetric imbeddings. Using this theorem, we solve the problem of quasiconformal extension from a one-parameter family of quasiconformal triangles of a special type that do not have a general estimate of quasiconformal convexity.